Inthispaper,anewquasi-interpolationwithradialbasisfunctionswhichsatis-fiesquadraticpolynomialreproductionisconstructedontheinfinitesetofequallyspaceddata.Anewbasisfunctionisconstructedbymakingconvolutionintegralwithaconstructedsplineandagivenradialbasisfunction.Inparticular,fortwicelydiffer-entiablefunctiontheproposedmethodprovidesbetterapproximationandalsotakescareofderivativesapproximation.